She may just not be interested in you. Not putting your arm around her isn't enough to completely turn someone off. There are certain factors that you have that you can't "screw up" on. It's just how you are. She may just not like how you are. If she's brushing you off and doesn't seem interested, move on and try someone new, but don't think you messed up because you didn't touch her. There probably wasn't anything you could do to get her interested in you anyway.